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The line L given by x 5 + y b = 1 passes through the point ( 13 , 32 ) . If the line K is parallel to L and has the equation x c + y 3 = 1 , then the distance between L and K is

Options

  1. A23 15 units
  2. B17 units
  3. C17 15 units
  4. D23 17 units

Correct answer

D. 23 17 units

Step-by-step solution

Since, line L passes through ( 13 , 32 ) ∴ 13 5 + 32 b = 1 ⇒ 32 b = 1 - 13 5 = - 8 5 ⇒ b = - 32 × 5 8 = - 20 ⇒ L : x 5 - y 20 = 1 Given, K : x c + y 3 = 1 is a line parallel to L = 0 ∴ The line K must have equation x 5 - y 20 = a o r   x 5 a - y 20 a = 1 On comparing with x c + y 3 = 1 , we get, - 20 a = 3 ,   c = 5 a ⇒ a = - 3 20 ,   c = - 15 20 ∴   Distance between the two lines is a - 1 1 25 + 1 400 = - 3 20 - 1 17 400 = 23 17 units

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